Question: Rewrite as a simplified fraction. ${0.3\overline{38} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 338.3838...\\ 10x &= 3.3838...\end{align*}}$ Subtracting the two equations, we have: ${990x = 335}$ ${x = \dfrac{335}{990}} $ ${x = \dfrac{67}{198}} $